As a current owner of a wakeboard boat and previous owner of a conventional bowlder I can give you some information from experience. First, some of the 'wake' versions of good bowriders are decent all around boats. The forward facing sterndrive makes them safe for surfing and the hull design and adjustable drive trim gets a bit more top speed, if you like to spend a lot of time maxed out. The forward drive however has a deeper draft than a conventional sterndrive so the argument that you can run shallower than an inboard wake boat does not hold up. Some have good built in ballast to get better wakes and you can always add more ballast to any boat to get the best wave the hull can give you.
With an inboard wake boat you get several other advantages and a couple disadvantages. For a family there are a couple good benefits to the wake boat. The swim deck is right at the water and there is usually no need to use a ladder to reboard when you've been swimming. For my family this is a huge benefit. Also, the boat is slightly bigger inside as the length of the boat does not include the removable swim deck and a bowlder has the drive hanging off the transom which adds to the overall length but adds no interior space. The normal draft of a wake boat is less than a sterndrive so you are generally better in shallow water unless you have trimmed up the drive, which hurts the steering on a conventional bowrider. The wake boat is designed to give smooth flow off the back of the hull so they generally have cleaner wakes for any type of boarding and a benefit to the smoother water flow is that your economy is actually better when running slow or at mid cruising speeds. Above 35 mph the economy is worse as the hull does not lift from the water as much so more wet area adds drag. We tend to cruise at 25-30 as there is less wind and it's quieter. Your use may be different.
Handling of the two types is different. The wake boat will turn much tighter and, when you are used to how it drives, is easier to park if there is no wind or current. You can park or maneuver well if there is wind or current but you need more skill in these conditions. If you like to drive or have some experience an inboard is not problem. If you have difficulty parking anyway a sterndrive bowrider might be better. My wife and kids have easily become experts purring the boat on the dock, even nose out. In rough water some wakevoats can give a more pounding ride. Some however, are excellent in rough water. Mine, a Sanger, is great in any rough water and gives a smoother ride than most bow riders as I can travel slower without the nose riding to high and the hull is very solid. It has a 16° deadrise at the transom. Others have even more but most have less.
I'm never going back to a bowrider but you really need to drive each and see what you think when you are in them. A test drive is really important. Also, most boat owners will think their brand and style is best because they bought it to suit them. Filter any advise with this in mind. Your kids are at a great age to enjoy bing out on the water a great deal. Enjoy.
